Abstract
This paper revisits an important, yet poorly understood, phenomenon of genetic optimisation, namely the mixing or juxtapositioning capacity of recombination, and its relation to selection. Mixing is a key factor in order to determine when a genetic algorithm will converge to the global optimum, or when it will prematurely converge to a suboptimal solution. It is argued that from a dynamical point of view, selection and recombination are involved in a kind of race against time: the number of instances of good building blocks is quickly increased from generation to generation by the selection phase, but in order to create optimal solutions these building blocks have to be juxtaposed by the crossover operator and this also takes some time to occur. If the selection of building blocks goes too fast — relative to the rate at which crossover can juxtapose or mix them — then the population will prematurely converge to a suboptimal solution. Previous work (Goldberg, Deb & Thierens, 1993) made a first step toward a better understanding of mixing in genetic algorithms, and also introduced the use of dimensional analysis in GA modelling. In this paper we extend this work by integrating some of the insights gained from the modelling of the dynamic behaviour of GAs on infinite populations (Mühlenbein & Schlierkamp-Voosen, 1993; Thierens & Goldberg, 1994; Bäck, 1995; Miller & Goldberg, 1995). The resulting dimensional model quantifies the allele-wise mixing process: it specifies the boundary in the GA parameter space between the region of reliable convergence at one side, and the region of premature convergence at the other. Although the model is limited to simple bit-wise mixing, the lessons learned from it are quite general and are also valid for more difficult, building-block based problems.
Preview
Unable to display preview. Download preview PDF.
References
Bäck T. (1995). Generalised Convergence Models for Tournament-and (Μ, λ)-Selection. Proceedings of the Sixth International Conference on Genetic Algorithms.
Goldberg D.E. (1989). Genetic Algorithms in Search, Optimisation and Machine Learning. Addison Wesley Publishing Company.
Goldberg D.E. (1994). First Flights at Genetic-Algorithm Kitty Hawk. IlliGAL Report No. 94008. University of Illinois at Urbana-Champaign, Illinois Genetic Algorithm Laboratory.
Goldberg D.E., & Deb K. (1991). A comparative analysis of selection schemes used in genetic algorithms. Proceedings of Foundations of Genetic Algorithms FOGA-I. ed. G. Rawlings. pp.69–93. Morgan Kaufmann.
Goldberg D.E., Deb K., & Thierens D. (1993). Toward a better understanding of mixing in genetic algorithms. Journal of the Society for Instrumentation and Control Engineers, SICE Vol.32, No.1 pp.10–16.
Holland J.H. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press.
Ipsen D.C.(1960). Units, dimensions, and dimensionless numbers. McGraw-Hill.
Miller B. L., & Goldberg D. E. (1995). Genetic algorithms, selection schemes, and the varying effects of noise IlliGAL Report No. 95009. Illinois Genetic Algorithm Laboratory. University of Illinois at Urbana-Champaign
Mühlenbein H. & Schlierkamp-Voosen D. (1993). Predictive Models for the Breeder Genetic Algorithm. I. Continuous Parameter Optimisation. Evolutionary Computation 1(1):25–49, MIT Press.
Rudnick M. (1992). Genetic Algorithms and Fitness Variance with an Application to the Automated Design of Artificial Neural Networks. Unpublished doctoral dissertation, Oregon Graduate Institute of Science and Technology, Beaverton.
Thierens D., & Goldberg D.E. (1993). Mixing in Genetic Algorithms. Proceedings of the Fifth International Conference on Genetic Algorithms ICGA-93. ed. S. Forrest, pp.38–45. Morgan Kaufmann.
Thierens D., & Goldberg D.E. (1994). Convergence Models of Genetic Algorithm Selection Schemes. Lecture Notes in Computer Science, Vol. 866: Parallel Problem Solving from Nature PPSN-III. Jerusalem (Il). eds. Y. Davidor, H.P. Schwefel, R. Männer, pp.119–129. Springer-Verlag.
Thierens D. (1995). Analysis and Design of Genetic Algorithms. PhD thesis, Dept. Electrical Engineering, Kath. Univ. Leuven, Belgium.
Vose M., & Liepins G. (1991). Punctuated Equilibria in Genetic Search. Complex Systems 5:31–44
Whitley D. (1993). An Executable Model of a Simple Genetic Algorithm. Foundations of Genetic Algorithms II. Morgan Kaufmann.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thierens, D. (1996). Dimensional analysis of allele-wise mixing revisited. In: Voigt, HM., Ebeling, W., Rechenberg, I., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN IV. PPSN 1996. Lecture Notes in Computer Science, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61723-X_990
Download citation
DOI: https://doi.org/10.1007/3-540-61723-X_990
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61723-5
Online ISBN: 978-3-540-70668-7
eBook Packages: Springer Book Archive